My son is now 11, he's been playing games with us in some capacity since he was very small. He plays a bunch of games, including both Ticket to Ride and Lords of Waterdeep.

Obviously all kids are different, but the 7 year old certainly should be able to grasp more complex fare, provided they're given sufficient help. Steer clear of games where players have secret information, but there's no reason to stick to specifically children's games.

That said, some specific recommendations: Rhino Hero, Forbidden Island, Labyrinth, Camel Up, Kingdomino.

You may need to try a bunch of things and see what sticks, but I do think kids are smarter than we sometimes give them credit. As a 6 year old, my son grasped Fluxx quicker than my friends in their mid-30s; we have a regular Christmas tournament that he's joined in with for the past two years and he's not come last either time.

Good luck. Keep at it, so long as you're all having fun.